Econ Papers Daily / 期刊论文
当死亡率跃升时：确定缴费型养老金计划的最优投资组合设计
When mortality jumps: optimal portfolio design for defined contribution pension schemes
摘要
This paper analyzes optimal portfolio allocation in defined contribution pension schemes under joint exposure to mortality and financial jump risks. We develop a continuous-time framework in which both mortality intensity and financial asset prices follow jump–diffusion dynamics, extending standard pension models with continuous mortality and diffusion-based markets. The member’s objective combines expected terminal wealth maximization with downside risk control via Conditional Value-at-Risk (CVaR), generating a time inconsistent stochastic control problem. We reformulate the problem as a bilevel optimization structure: for a fixed CVaR threshold, the inner problem reduces to a standard stochastic control problem, while the outer problem becomes a one-dimensional convex minimization. Using inf-convolution regularization and a probabilistic gradient representation derived from Feynman–Kac theory, we establish existence, uniqueness, and differentiability properties of the value function, thereby ensuring analytical tractability of the model. These results provide a rigorous foundation for numerical implementation through semi-Lagrangian schemes combined with gradient-based optimization. Numerical experiments quantify the impact of mortality jumps and mortality-linked derivatives on optimal portfolio policies. In particular, short-maturity longevity derivatives enhance downside protection, and appropriately structured hedging of mortality jump risk improves tail risk measures without reducing expected terminal wealth.
中文摘要
本文分析了在同时面临死亡风险和金融跳跃风险的情况下，确定缴费型养老金计划中的最优投资组合配置。我们构建了一个连续时间框架，其中死亡强度与金融资产价格均服从跳跃—扩散动态，从而在连续死亡率和基于扩散的市场方面拓展了标准养老金模型。成员的目标将期望终端财富最大化与通过条件风险价值（CVaR）进行的下行风险控制相结合，形成了一个时间不一致的随机控制问题。我们将该问题重新表述为双层优化结构：对于固定的CVaR阈值，内层问题简化为标准随机控制问题，而外层问题则变为一维凸最小化问题。利用下卷积正则化以及由Feynman–Kac理论导出的概率梯度表示，我们建立了值函数的存在性、唯一性和可微性性质，从而确保了模型的解析可处理性。这些结果为通过半拉格朗日格式结合基于梯度的优化进行数值实现提供了严谨基础。数值实验量化了死亡率跳跃和死亡率关联衍生品对最优投资组合策略的影响。特别地，短期限长寿衍生品增强了下行保护，而对死亡率跳跃风险进行适当结构化的对冲可在不降低期望终端财富的情况下改善尾部风险度量。